Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-06T00:59:23.533Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on compactifications and semi-normal spaces

Published online by Cambridge University Press:  09 April 2009

R. A. Alo  and
H. L. Shapiro
R. A. Alo
Affiliation:
The Carnegie Institute of Technology
H. L. Shapiro
Affiliation:
The Pennsylvania State University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently Orrin Frink (see [2]) gave a neat internal characterization of Tychonoff or completely regular T spaces. This characterization was given in terms of the notion of a normal base for the closed sets of a space X. A normal base for the closed sets of a space X is a base which is a disjunctive ring of sets, disjoint members of which may be separated by disjoint complements of members of . In a normal space the ring of closed sets is a normal base.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 1 , February 1968 , pp. 102 - 108
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Freudenthal, H., ‘Kompaktisierungen und bikompaktisierungen’, Indag. Math. 13 (1951), 184–192.CrossRefGoogle Scholar
[2]Frink, Orrin, ‘Compactifications and semi-normal spaces’, Amer. J. Math. 86 (1964), 602–607.CrossRefGoogle Scholar
[3]Gould, G. G., ‘A Stone-Cech-Alexandroff compactification and its application to measure theory’, Proc. London Math. Soc. 14 (1964), 221–244.CrossRefGoogle Scholar
[4]Njastad, Olav, ‘On Wallman-type compactifications’, Math.Z. 91 (1966), 267–276.CrossRefGoogle Scholar
[5]Smirnov, Yu. M., ‘On proximity spaces’, Mat. Sb. N. S. 31 (1952), 543–574 (Russian).Google Scholar
[6]Alfsen, and Fenstad, J., ‘A note on completion and compactification’, Math. Scand. 8 (1960), 97–104.CrossRefGoogle Scholar
[7]Fan, Ky and Gottesman, N., ‘On compactifications of Freundenthal and Wallman’, Indag. Math. 14 (1952), 504–510.CrossRefGoogle Scholar
[8]Gillman, L. and Jerison, M., ‘Rings of continuous functions’, (Princeton, Van Nostrand, 1960).CrossRefGoogle Scholar
[9]Kelley, J. L., General Topology (New York, Van Nostrand, 1955).Google Scholar
[10]Wallman, H., ‘Lattices and topological spaces’, Annals of Math. 39 (1938), 112–126.CrossRefGoogle Scholar